ASTRONOMY AND ASTROPHYSICS Dark matter in early-type spiral

Astron. Astrophys. 342, 671–686 (1999)

ASTRONOMY AND ASTROPHYSICS

Dark matter in early-type spiral galaxies: the case of NGC 2179 and of NGC 2775?,?? E.M. Corsini1 , A. Pizzella2 , M. Sarzi3 , P. Cinzano3 , J.C. Vega Beltrán4 , J.G. Funes S.J.3 , F. Bertola3 , M. Persic5 , and P. Salucci6 1 2 3 4 5 6

Osservatorio Astrofisico di Asiago, Dipartimento di Astronomia, Università di Padova, via dell’Osservatorio 8, I-36012 Asiago, Italy European Southern Observatory, Alonso de Cordova 3107, Casilla 19001, Santiago 19, Chile Dipartimento di Astronomia, Università di Padova, vicolo dell’Osservatorio 5, I-35122 Padova, Italy Osservatorio Astronomico di Padova, Telescopio Nazionale Galileo, vicolo dell’Osservatorio 5, I-35122 Padova, Italy Osservatorio Astronomico di Trieste, via G.B. Tiepolo 11, I-34131 Trieste, Italy SISSA, via Beirut 2–4, I-34013 Trieste, Italy

Received 8 June 1998 / Accepted 3 November 1998

Abstract. We present the stellar and ionized-gas velocity curves and velocity-dispersion profiles along the major axis for six early-type spiral galaxies. Two of these galaxies, namely NGC 2179 and NGC 2775, are particularly suited for the study of dark matter halos. Using their luminosity profiles and modeling their stellar and gaseous kinematics, we derive the mass contributions of the luminous and the dark matter to the total potential. In NGC 2179 we find that the data (measured out to about the optical radius Ropt ) unambiguously require the presence of a massive dark halo. For the brighter and bigger object NGC 2775, we can rule out a significant halo contribution at radii R < ∼ 0.6 Ropt . Although preliminary, these results agree with the familiar mass distribution trend known for late-type spirals of comparable mass. Key words: galaxies: individual: NGC 2179 – galaxies: individual: NGC 2775 – galaxies: kinematics and dynamics – galaxies: spiral – cosmology: dark matter

1. Introduction Recent analyses of extended rotation curves (RCs) of late-type spiral galaxies (Persic, Salucci & Stel 1996) have confirmed that in spirals of all luminosities a substantial dark matter (DM) component is detectable already in the optical region. The effect is stronger at lower luminosities: the dark-to-visible mass ratio at the optical radius Ropt 1 scales with luminosity ∝ L−0.7 . Send offprint requests to: E.M. Corsini ? Based on observations carried out at ESO, La Silla (Chile) (ESO N. 52, 1-020) and on observations obtained with the VATT: the Alice P. Lennon Telescope and the Thomas J. Bannan Astrophysics Facility. ?? Tables 4 to 42 are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/Abstract.html. Correspondence to: ([email protected]) 1 Ropt = 3.2 RD is the radius encompassing the 83% of the total integrated light. RD is the scale-length of the exponential surface

For early-type spirals the status of our knowledge is different. The RCs presently available for these objects are fragmentary (in particular in the nuclear regions), and only extend to < ∼ 2 RD (see Rubin et al. 1985). Consequently, detailed mass decomposition have so far not been possible for these systems. In particular, it is not known whether dark halos are unambiguously present also in early-type spirals. It may be conjectured that for a given V (Ropt ) the DM fraction within the optical size is smaller in early than in late-type spirals: this, because in an early spiral the conspicuous stellar bulge, with (M/L)bulge > ∼ 3(M/L)disk , can supply a mass compact enough to make the rotation velocity higher than (see Rubin et al. 1985), and the velocity profile different from, that of a late spiral of similar luminosity. In this case, the derivation of the halo parameters would be more uncertain for early than for late types: in fact, at small radii not two mass components (disk + halo, like in Sc-Sd galaxies), but three mass components (bulge + disk + halo) will have locally similar (solid-body like) behaviors. So for non-extended RC data the mass solution of an Sa galaxy would be degenerate even within the maximum-disk solution. In this paper we present the velocity and velocity-dispersion profiles of the stars and the ionized gas, measured along the major axis, for six early-type spirals. The six selected galaxies (Table 1) were already known to show emission lines and their photometric properties were known. Of these, 5 had already been observed spectroscopically by Rubin et al. (1985), who obtained the RCs of the ionized gas, and photometrically by Kent (1988). NGC 2179 was the only galaxy in our sample still lacking spectroscopical and photometrical observations. To the originally observed sample belonged the early-type spiral NGC 3593 too. Its stellar and the gaseous kinematics, found to exhibit a star vs. star counterrotation, is presented and discussed by Bertola et al. (1996). Three-component models (bulge brightness distribution I(r) = I(0) e−r/RD . For a Freeman (1970) disk, Ropt corresponds to the de Vaucouleurs 25 B-mag arcsec−2 photometric radius.

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E.M. Corsini et al.: Dark matter in Sa galaxies: NGC 2179 and NGC 2775

Table 1. Parameters of the sample galaxies. object [name] (1) NGC 2179 NGC 2775 NGC 3281 IC 724 NGC 4698 NGC 4845

type [RSA] [RC3] (2) (3)

BT [mag] (4)

P.A. [◦ ] (5)

◦

[ ] (6)

V [km s−1 ] (7)

V0 [km s−1 ] (8)

D [Mpc] (9)

scale [pc00−1 ] (10)

R25 [00 ] (11)

far Rstar [00 ] (12)

far Rgas 00 [ ] (13)

Sa Sa(r) Sa Sa Sa Sa

13.22 11.03 12.70 13.4 11.46 12.10

170 163 138 60 170 75

51 44 69 55 70 72

2885±10 1350±10 3380±10 5974±10 992±10 1084±10

2673 1180 3098 5853 909 980

35.6 15.7 41.3 78.0 12.1 13.1

172.6 76.1 200.2 378.2 58.7 63.5

51 128 99 70 119 150

41 100 86 62 76 87

54 77 50 56 113 100

.SAS0.. .SAR2.. .SAS2P* .S..1.. .SAS2.. .SAS2./

i

time [h ] (14) 8.5 6.5 6.5 2.0 4.7 4.0

Notes – Col.(2): classification from RSA (Sandage & Tamman 1981). Col.(3): classification from RC3 (de Vaucouleurs et al. 1991). Col.(4): total observed blue magnitude from RC3 except for IC 724 (RSA). Col.(5): observed position angle. Col.(6): inclination from Rubin et al. (1985) except for NGC 2179 (Tully 1988). Col.(7): heliocentric velocity of the galaxy derived as center of symmetry of the gas RC. Col.(8): systemic velocity derived from V corrected for the motion of the Sun with respect of the Local Group by ∆V = 300 cos b sin l. Col.(9): distance obtained as V0 /H0 with H0 = 75 km s−1 Mpc−1 . Col.(11): radius of the 25 B−mag arcsec−2 isophote from RC3. Col.(12): radius of the farthest measured stellar velocity. Col.(13): radius of the farthest measured gas velocity. Col.(14): total integration time of the spectroscopic observation.

+ disk + halo) based on observed photometry and kinematics are obtained for two galaxies of the sample: NGC 2179 and NGC 2775.

2. Observations and data reduction 2.1. The spectroscopic observations The spectroscopic observations of our sample galaxies were carried out at the ESO 1.52-m Spectroscopic Telescope at La Silla on February 15–19, 1994. The telescope was equipped with the Boller & Chivens Spectrograph. The No. 26 grating with 1200 grooves mm−1 was used in the first order in combination with a 2.00 5 × 4.0 2 slit. It ˚ between about 5200 A ˚ yielded a wavelength coverage of 1990 A −1 ˚ ˚ and about 7190 A with a reciprocal dispersion of 64.80 A mm . The instrumental resolution was derived measuring after calibration the FWHM of 22 individual emission lines distributed all over the spectral range in the 10 central rows of a comparison spectrum. We checked that the measured FWHM’s did not depend on wavelength, and we found a FWHM mean value of ˚ This corresponds to σ = 0.99 A ˚ (i.e., 51 km s−1 at 2.34 A. −1 ˚ ˚ 5800 A and 46 km s at 6400 A). The adopted detector was the No. 24 2048×2048 Ford CCD, which has a 15 × 15 µm2 pixel size. After an on-chip binning of 3 pixels along the spatial ˚ × 2.00 43. direction, each pixel of the frame corresponds to 0.97 A The long-slit spectra of all the galaxies were taken along their optical major axes. At the beginning of each exposure the galaxy was centered on the slit using the guiding camera. Repeated exposures (typically of 3600 s each) did ensure several hours of effective integration without storing up too many cosmic rays. Some long-slit spectra of 8 late-G or early-K giant stars, obtained with the same instrumental setup, served as templates in measuring the stellar kinematics. Their spectral classes range from G8III to K4III (Hoffleit & Jaschek 1982). The typical value of the seeing FWHM during the observing nights, measured by the La Silla Differential Image Motion

Monitor (DIMM), was 100 − 1.00 5. Comparison helium-argon lamp exposures were taken before and after every object exposure. The logs of the spectroscopic observations of galaxies and template stars are reported in Tables 2 and 3, respectively. 2.1.1. Data reduction Using standard MIDAS2 routines, all the spectra were bias subtracted, flat-field corrected by quartz lamp exposures, and cleaned from cosmic rays. Cosmic rays were identified by comparing the counts in each pixel with the local mean and standard deviation, and then corrected by substituting a suitable value. A small misalignment was present between the CCD and the slit. We measured a difference of ∆Y ' 1.4 pixel between the positions of the center of the stellar continuum near the blue and red edge of the spectra. When measuring the stellar kinematics, the tilt had to be removed. This was done by rotating the spectra by a suitable angle (θ = 0.◦ 04) before the wavelength calibration. We noticed however that the sharp line profile of the emission lines was spoiled by the rotating algorithm. For this reason no rotation was applied when measuring the ionized-gas kinematics. The wavelength calibration was done using the MIDAS package XLONG. We determined the velocity error possibly introduced by the calibration measuring the ‘velocity curve’ of a sample of 24 OH night-sky emission lines distributed all over the spectral range. The velocity did not show any significant dependence on radius, indicating that the wavelength rebinning had been done properly. We found a mean deviation from the predicted wavelengths (Osterbrock et al. 1996) of 2 km s−1 . After calibration, the different spectra obtained for a given galaxy were co-added using their stellar-continuum centers as reference. For each spectrum the center was assumed as the center of the Gaussian fitting the mean radial profile of the stellar 2

MIDAS is developed and maintained by the European Southern Observatory.

E.M. Corsini et al.: Dark matter in Sa galaxies: NGC 2179 and NGC 2775 Table 2. Log of spectroscopic observations (galaxies). object [name] (1)

Table 3. Log of spectroscopic observations (template stars).

date [d m y] (2)

U.T. [h m] (3)

time [s] (4)

object [name] (1)

NGC 2179 NGC 2179 NGC 2179 NGC 2179 NGC 2179 NGC 2179 NGC 2179 NGC 2179

15 Feb 1994 15 Feb 1994 16 Feb 1994 17 Feb 1994 18 Feb 1994 18 Feb 1994 19 Feb 1994 19 Feb 1994

01 24 02 32 01 17 01 41 00 26 01 35 00 19 01 27

3600 3600 5400 3600 3600 3600 3600 3600

HR 2035 HR 2035 HR 2035 HR 2035 HR 2035 HR 2035 HR 2035

NGC 2775 NGC 2775 NGC 2775 NGC 2775 NGC 2775 NGC 2775

15 Feb 1994 15 Feb 1994 16 Feb 1994 17 Feb 1994 17 Feb 1994 18 Feb 1994

04 10 05 17 03 56 02 47 03 53 02 41

3600 3600 5400 3600 3600 3600

NGC 3281 NGC 3281 NGC 3281 NGC 3281 NGC 3281 NGC 3281

16 Feb 1994 16 Feb 1994 17 Feb 1994 18 Feb 1994 19 Feb 1994 19 Feb 1994

04 39 06 14 05 02 03 50 02 34 03 40

5400 3600 3600 3600 3600 3600

IC 724 IC 724

17 Feb 1994 17 Feb 1994

06 16 07 21

3600 3600

NGC 4698 NGC 4698 NGC 4698 NGC 4698

16 Feb 1994 16 Feb 1994 18 Feb 1994 19 Feb 1994

07 22 08 28 07 17 07 42

3600 3600 3600 6000

NGC 4845 NGC 4845 NGC 4845 NGC 4845

15 Feb 1994 15 Feb 1994 17 Feb 1994 18 Feb 1994

07 02 08 08 05 02 08 25

3600 3600 3600 3600

Notes – Cols.(2–3): date and time of start of exposure. Col.(4): exposure time.

continuum. The contribution of the sky was determined from the edges of the resulting galaxy frames and then subtracted. 2.1.2. Measuring the gas kinematics The ionized-gas velocities (vg ) and velocity dispersions (σg ) were measured by means of the MIDAS package ALICE. We ˚ the Hα line measured the [N II] lines (λλ 6548.03, 6583.41 A), ˚ ˚ (λ 6562.82 A), and the [S II] lines (λλ 6716.47, 6730.85 A), where they were clearly detected. The position, the FWHM, and the uncalibrated flux F of each emission line were determined by interactively fitting one Gaussian to each line plus a polynomial to its local continuum. The center wavelength of the fitting Gaussian was converted into velocity in the optical convention v = cz; then the standard heliocentric correction was applied. The Gaussian FWHM was corrected for the instrumental FWHM, and then converted into the velocity dispersion σ. In the regions where the intensity of the emission lines was

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type [BSC] (2)

date [d m y] (3)

U.T. [h m] (4)

time [s] (5)

G8III G8III G8III G8III G8III G8III G8III

15 Feb 1994 17 Feb 1994 17 Feb 1994 17 Feb 1994 17 Feb 1994 19 Feb 1994 19 Feb 1994

00 53 00 04 00 07 00 10 00 16 00 07 00 09

2 2 3 4 3 2 3

HR 2429 HR 2429 HR 2429

K1III K1III K1III

18 Feb 1994 18 Feb 1994 18 Feb 1994

00 08 00 11 00 14

2 2 3

HR 2443

K1III

16 Feb 1994

00 25

3

HR 2503 HR 2503 HR 2503 HR 2503 HR 2503

K4III K4III K4III K4III K4III

16 Feb 1994 16 Feb 1994 16 Feb 1994 16 Feb 1994 16 Feb 1994

00 35 00 38 00 41 00 46 00 49

4 4 4 4 8

HR 3431

K4III

15 Feb 1994

03 52

4

HR 5100 HR 5100

K0III K0III

19 Feb 1994 19 Feb 1994

09 29 09 32

10 7

HR 5196 HR 5196 HR 5196

K0.5III K0.5III K0.5III

16 Feb 1994 16 Feb 1994 16 Feb 1994

09 33 09 38 09 43

4 15 10

HR 5315 HR 5315 HR 5315

K3III K3III K3III

15 Feb 1994 15 Feb 1994 15 Feb 1994

09 14 09 17 09 21

4 3 3

HR 5601 HR 5601 HR 5601 HR 5601

K0.5III K0.5III K0.5III K0.5III

15 Feb 1994 15 Feb 1994 15 Feb 1994 15 Feb 1994

09 29 09 32 09 35 09 39

3 4 4 10

Notes – Col.(2): spectral class of the template star from The Bright Star Catalogue (Hoffleit & Jaschek 1982). Cols.(3–4): date and time of start of exposure. Col.(5): exposure time.

low, we binned adjacent spectral rows in order to improve the signal-to-noise ratio, S/N , of the lines. We expressed the variation of the r.m.s. velocity error δv as a function of the relevant line S/N ratio. In order to find the expression for δv = δv(S/N ), we selected the same 16 night-sky emission lines in the spectra of NGC 2775, NGC 3281, IC 724 and NGC 4845. Such night-sky emissions were chosen to have ˚ different intensities and different wavelengths between 6450 A ˚ and 6680 A (i.e. the wavelength range of the observed emission lines of the ionized gas) in the four spectra. We derived the sky spectra by averaging several rows along the spatial direction in a galaxy-light free region. Using the above package, we interactively fitted one Gaussian emission plus a polynomial continuum to each selected sky line and its local continuum. We derived the flux F and the FWHM of the sample lines, taking the ratio F/FWHM as the signal S. For each galaxy spectrum the noise N was defined as the r.m.s. of the counts measured in

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Fig. 1. The variation of the r.m.s. velocity error δv as a function of the signal-to-noise ratio S/N . The symbols (triangles, circles, squares and crosses) represent the r.m.s. δv of the quadratic polynomials fitting the ‘velocity curves’ of the same 16 night-sky emission lines selected in 4 different spectra (NGC 2775, NGC 3281, IC 724 and NGC 4845 respectively) as a function of the relevant S/N ratio of the lines. The full line represents the power law fitting the data. In the insert the data are plotted in logarithmic scale

regions of the frame where the contributions of both the galaxy and the sky lines were negligible. The resulting S/N range was large (1 ≤ S/N ≤ 50). For each sample emission line we then measured, by means of an automatic procedure, the night-sky ‘velocity curve’ along the full slit extension. The wavelengths of the emissions were evaluated with Gaussian fits and then converted to velocities. The radial profiles of the sky-line velocities were then fitted by quadratic polynomials. We assumed the r.m.s. of the fit to each ‘velocity curve’ to be the 1σ velocity error. Fig. 1 shows the good agreement between the distributions of the (S/N, δv) measurements taken in the 4 different spectra. In log-log scale, the (S/N, δv) relation is well represented by a straight line, that corresponds to: −0.90 S km s−1 (1) δv = 60.4 N (least-squares fit). This result agrees with Keel’s (1996) relation δv ∝ (S/N )−1 , based on numerical simulations. Once the relevant S/N ratio of the emission had been derived, we obtained δv for each velocity measurement of the ionized-gas component by means of Eq. 1. The gas velocities derived independently from different emission lines are in mutual agreement within their errors δv. The ionized-gas velocities and velocity dispersions from ˚ [S II] (λλ 6716.47, 6730.85 A), ˚ [N II] (λλ 6548.03, 6583.41 A), and Hα are reported in: Tables 4–7 for NGC 2179; Tables 10–14 for NGC 2775; Tables 17 – 21 for NGC 3281; Tables 24–26 for

IC 724; Tables 29–33 for NGC 4698; and Tables 36–40 for NGC 4845. Each table reports the galactocentric distance r in arcsec (Col. 1), the observed heliocentric velocity v and its error δv in km s−1 (Col. 2), the velocity dispersion σ in km s−1 (Col. 3), the number n of spectrum rows binned along the spatial direction (Col. 4), and the signal-to-noise ratio S/N of the emission line (Col. 5). The Hα, [N II] and [S II] kinematics of the sample objects are plotted in Figs. 2–4. The final ionized-gas kinematics is obtained by averaging, at each radius, the gas velocities and velocity dispersions derived independently from the different emission lines. The gas velocity (vg ) and velocity error (δvg ) are respectively the 1/σv2 weighted mean velocity and its uncertainty. The gas velocity dispersion (σg ) and velocity-dispersion error (δσg ) are the mean velocity dispersion and its uncertainty. (No error is given when only one velocity dispersion measurement is available.) The kinematics of the ionized gas is reported in: Table 8 for NGC 2179; Table 15 for NGC 2775; Table 22 for NGC 3281; Table 27 for IC 724; Table 34 for NGC 4698; and Table 41 for NGC 4845. Each table reports the galactocentric distance r in arcsec (Col. 1), the mean heliocentric velocity vg and its error δvg in km s−1 (Col. 2), the mean velocity dispersion σg and its error δσg in km s−1 (Col. 3). The ionized-gas velocity and velocity-dispersion profiles are plotted in Fig. 5 for all our galaxies. 2.1.3. Measuring the stellar kinematics The stellar velocities (v? ) and velocity dispersions (σ? ) of the sample galaxies were measured from the absorption lines in ˚ and 6200 A. ˚ We the wavelength range between about 5200 A used an interactive version of the Fourier Quotient Method (Sargent et al. 1977) as applied by Bertola et al. (1984). The K0III star HR 5100 was taken as template: it has a radial velocity of −0.9 km s−1 (Wilson 1953) and a rotational velocity of 10 km s−1 (Bernacca & Perinotto 1970). The spectra of the galaxies and the template star were rebinned to a logarithmic wavelength scale, continuum subtracted, and masked at their edges by means of a cosine bell function of 20% length. At each radius the galaxy spectrum was assumed to be the convolution of the template spectrum with a Gaussian broadening function characterized by the parameters γ, v? and σ? . They respectively represent the line strength of the galaxy spectrum relative to the template’s, and the line-ofsight stellar velocity and velocity dispersion. The parameters of the broadening function, and consequently the stellar kinematics, were obtained by a least-squares fitting in the Fourier space of the broadened template spectrum to the galaxy spectrum in the wavenumber range [kmin , kmax ] = [5, 440]. In this way we rejected the low-frequency trends (corresponding to k < 5) due to the residuals of continuum subtraction and the high-frequency noise (corresponding to k > 440) due to the instrumental resolution. (The wavenumber range is important in particular in the Fourier fitting of lines with non-Gaussian profiles, see van der Marel & Franx 1993 and Cinzano & van der Marel 1994). In deriving the above kinematical properties, the


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Fig. 2. NGC 2179 and NGC 2775 observed major-axis velocity curves and velocity dispersion profiles of ionized gas. The kinematics measured from the Hα line is represented by open squares (u t). The crosses (+) and the open triangles (4) refer to the data obtained from the [N II] ˚ The times (×) and the reversed triangles (5) represent kinematics desumed from the [S II] (λλ 6716.47, 6730.85 A) ˚ (λλ 6548.03, 6583.41 A) lines. For the velocities only the errors greater than symbols are plotted

˚ and 5884.0 < λ < 5900.0 A ˚ regions 5569.0 < λ < 5585.0 A were masked because of contamination from bad subtraction of ˚ and Na I the night-sky emission lines of [O I] (λ 5577.34 A) ˚ (λ 5889.95 A). The measured stellar kinematics is reported in: Table 9 for NGC 2179; Table 16 for NGC 2775; Table 23 for NGC 3281; Table 28 for IC 724; Table 35 for NGC 4698; and Table 42 for NGC 4845. Each table reports the galactocentric distance r in arcsec (Col. 1), the heliocentric velocity v? and its error δv? in

km s−1 (Col. 2), the velocity dispersion σ? and its error δσ? in km s−1 (Col. 3). The stellar velocity and velocity-dispersion profiles are plotted in Fig. 5. 2.2. The photometric observations The observation in the Cousin R−band of NGC 2179 was performed on March 11, 1997 at the 1.83-m Vatican Advanced Technology Telescope (VATT) at Mt. Graham International O-

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Fig. 3. Same as in Fig. 2, but for NGC 3281 and IC 724

bservatory. A back-illuminated 2048×2048 Loral CCD with 15×15 µm2 pixels was used as detector at the aplanatic Gregorian focus, f/9. It yielded a field of view of 6.0 4 × 6.0 4 with an image scale of 0.00 4 pixel−1 after a 2 × 2 pixel binning. The gain and the readout noise were 1.4 e− ADU−1 and 6.5 e− respectively. We obtained 3 images of 120 s with the R 3.48-inch square filter. The data reduction was carried out using standard IRAF3 routines. The images were bias subtracted and then flat-field 3

IRAF is distributed by the National Optical Astronomy Observatories which are operated by the Association of Universities for Research

corrected. They were shifted and aligned to an accuracy of a few hundredths of a pixel using field stars as reference. After checking that the point spread functions (PSFs) in the images were comparable, they were averaged to obtain a single R image. The cosmic rays were identified and removed during the averaging routine. A Gaussian fit to the intensity profile of field stars in the resulting image allowed us to estimate a seeing PSF FWHM of 1.00 8.

in Astronomy (AURA) under cooperative agreement with the National Science Foundation.


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Fig. 4. Same as in Fig. 2, but for NGC 4698 and NGC 4845

The sky subtraction and the elliptical fitting to the galaxy isophotes were performed by means of the Astronomical Images Analysis Package (AIAP: Fasano 1990). The sky level was determined by a polynomial fit to surface brightness in frame regions not contaminated by galaxy light; then it was subtracted out from the total signal. The isophote fitting was performed masking the frame’s bad columns and the bright field stars. We then obtained surface brightness, ellipticity, major-axis position angle, and the cos 4θ Fourier coefficient of the isophote’s deviations from elliptical as a function of radius along the major axis. No photometric standards were observed. Thus the ab-

solute calibration was made using the photometric quantities edited by Lauberts & Valentijn (1989) in the same band. We set the surface brightness of an isophote with semi-major axis of a = 20.00 6 to the value µ = 21.23 R-mag arcsec−2 .

3. The stellar and ionized gas kinematics The resulting kinematics of all our galaxies are shown in Fig. 5. The plotted velocities are as observed (no inclination correction is applied). In the following we briefly discuss each individual object. At each radius, V? (≡ |v? − V |) and Vg (≡ |vg − V |)

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Fig. 5. Major-axis observed velocity curves and velocity dispersion profiles of the stellar (filled circles) and the gaseous (open circles) components for the sample galaxies. For the velocities the errorbars smaller than symbols are not plotted


are the observed rotation velocities of the stars and the ionized gas, respectively. NGC 2179. The gas and stellar kinematics respectively extend to 5000 (8.6 kpc) and 4000 (6.9 kpc) on either side of the nucleus. Outwards of 4000 , the stellar and the gas radial velocities are comparable. Stars. In the inner 1000 (1.7 kpc), V? increases to ∼ 100 km s−1 . At the center σ? ∼ 170 km s−1 ; away from the nucleus it remains high (σ? ≥ 100 km s−1 ), and possibly even rises. Gas. Vg has a steeper gradient than V? , reaching a value of Vg = 190 km s−1 at |r| ∼ 600 (1.0 kpc). σg is strongly peaked (∼ 150 km s−1 ) at the center; at |r| > 600 it drops rapidly to σg ' 30 km s−1 . A circumnuclear Keplerian disk of ionized gas has been recently discovered in the center of NGC 2179 by Bertola et al. (1998a) by means of optical ground-based observations. By modeling the motion of the gaseous disk they inferred the presence of a central mass concentration of 109 M . NGC 2775. The gas and stellar kinematics is measured out to 8000 (6.1 kpc) from the center. Stars. V? increases almost linearly with radius, up to about 130 km s−1 at |r| ∼ 2200 (1.7 kpc); for 2200 ≤ |r| ≤ 3000 it remains approximately constant; further out it increases to 185 km s−1 and then flattens out. At −3000 ≤ r ≤ +2000 , σ? > 150 km s−1 ; farther out it declines to ∼ 40 km s−1 and ∼ 100 km s−1 in the SE and NW side, respectively. Gas. The gas behaves differently in the two regions |r| ≤ 2000 (1.5 kpc) and |r| > 2000 . The [N II] λ6583.41 line (the only emission line detected in both regions, see Fig. 2) shows the presence of two kinematically distinct gas components, named component (i) and (ii). Component (i) rotates with the same velocity as the stars but with a lower velocity dispersion; component (ii) 00 rotates faster than the stars for 0 > r > ∼ −15 (1.1 kpc). Both components show up simultaneously in the spectrum only at |r| ' 1400 , where a double peak in the emission line is clearly detected. σg peaks (160 km s−1 ) at the center and rapidly drops to ∼ 30 km s−1 off center. 00

NGC 3281. The stellar kinematics extends to 90 (18 kpc) and 6000 (12 kpc) in the SE and the NW side, respectively. The gas kinematics can only be measured within 5000 (10 kpc) on each side of the nucleus. Stars. The stars exhibit a rather shallow rotation gradient: at r = 1000 (2 kpc), V? ∼ 100 km s−1 . At the center σ? ∼ 180 km s−1 ; off center it decreases to, respectively, ∼ 70 km s−1 in the SE side and ∼ 50 km s−1 in the NW side. Gas. Vg has a steep gradient, reaching 150 km s−1 at 1000 and then 200 km s−1 at 2000 (4 kpc). At the center σg ∼160 km s−1 , while at |r| > 2000 it falls to ∼50 km s−1 ; σg ∼ σ? for |r| < 1000 .

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IC 724. The stellar kinematics is observed out to 6000 (22.7 kpc) and 4000 (15.1 kpc) in the SW and NE sides, respectively. The ionized-gas kinematics extends to 6000 on each side of the nucleus. For |r| > 2000 (7.6 kpc), the gas and stellar kinematics are similar. For |r| < 2000 , σg is centrally peaked at ∼ 180 km s−1 , remaining lower than σ? . Stars. V? increases linearly up to ∼ 200 km s−1 in the inner 800 (3.0 kpc), followed by a drop to ∼ 170 km s−1 between 800 and 1500 on both sides of the nucleus; further out it rises to ∼ 240 km s−1 at 2000 , and then remains constant. At the center σ? ∼ 210 km s−1 , then off the nucleus it decreases to ∼ 50 km s−1 . Gas. Vg has a steeper gradient than V? , peaking at 300 km s−1 at about 800 ; then it decreases, becoming Vg ∼ V? at 2000 . The Hα shows steeper central RC gradient and lower velocity dispersion than [N II] and [S II] (see Fig. 3). This feature is probably due to the lower V? : the Hα absorption does not have the same central wavelength as the emission, and hence it shifts the resulting peak toward higher rotation velocities. NGC 4698. The stellar and ionized-gas kinematics are measured out to 7500 (4.4 kpc) and 10000 (5.9 kpc) on each side of the nucleus, respectively. Stars. In the innermost 1000 (0.6 kpc) the stars have zero rotation; at outer radii, V? is less steep than Vg ; only for |r| > 4000 (2.3 kpc) are V? ∼ Vg and σ? ∼ σg . The profile of σ? is radially asymmetric: in the SE side it shows a maximum of ∼ 150 km s−1 at 900 (0.5 kpc), then it decreases outwards to ∼ 50 and 30 km s−1 at 3000 (1.8 kpc) in the SE and NW sides, respectively. The measured zero rotation plateau is explained by Bertola et al. (1998b) as due to the presence of an orthogonalrotating bulge. Gas. Vg increases to ∼130 km s−1 in the inner 1800 (1.1 kpc); then it increases more gradually reaching ∼200 km s−1 at 6000 (3.5 kpc), and stays approximately constant farther out. In the inner ±700 (±0.4 kpc, roughly coinciding with the absorption lines region) σg has a 75 km s−1 plateau, while at larger radii it drops to σg ≤ 50 km s−1 . NGC 4845. The stellar and ionized-gas kinematics are measured out to 7000 (4.4 kpc) in the SW side, and out to 9000 (5.7 kpc) in the NE side. Stars. V? has a shallower gradient than Vg : it reaches 60 km s−1 at 800 (0.5 kpc), and further out it increases slowly, reaching the Vg at ∼ 6000 (3.8 kpc). The velocity dispersion is constant, σ? ∼ 60 km s−1 (in the SW side it drops to 30 km s−1 for r > 4000 ). Gas. Vg reaches ∼180 km s−1 at 1400 (0.9 kpc), to decrease and remain constant at 150 km s−1 farther out. For |r| < 1000 (0.6 kpc) σg ' 80 km s−1 , then it rapidly falls to < 30 and ∼ 40 km s−1 in the SW and NE sides, respectively; farther out the behavior of σg is more uncertain, due to a considerable scatter of the measurements from different lines: along the NW side

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σg ∼ 40 km s−1 , while along the SE side σg slowly decreases to ∼ 30 km s−1 . The triaxiality of the bulge of NGC 4845 has been detected by Bertola, Rubin & Zeilinger (1989) and discussed by Gerhard, Vietri & Kent (1989). The RCs and velocity-dispersion profiles of both the ionized gas and the stars in our Sa galaxies show a rich diversity of kinematical properties. V? has shallower gradient than Vg at the center, while V? = Vg at the last measured radius, in all our sample galaxies. For NGC 2179, NGC 2775, NGC 3593, NGC 4698 and NGC 4845, the gas RCs remain flat after a monotonic rise to a maximum [whose observed values range between ∼ 120 km s−1 (as for NGC 3593) and ∼ 190 km s−1 (as for NGC 2179, NGC 2775)], or rise monotonically to the farthest observed radius (as for NGC 3281 and IC 724: in the latter after an initial peak at ∼ 290 km s−1 ). Stellar counterrotation and orthogonal rotation have been found in NGC 3593 (Bertola et al. 1996) and NGC 4698 (Bertola et al. 1998b) respectively. The observed σ? exceeds 100 km s−1 for several kpc in the innermost regions, peaking at values ranging between 130 km s−1 (as in NGC 4698) and 210 km s−1 (as in IC 724); the only exception is NGC 4845 with σ? ∼ 70 km s−1 at all observed radii. There are sample galaxies whose σg is low at all radii, reaching a central maximum of ∼ 80 km s−1 (NGC 4698, NGC 4845) or remaining flattish at ∼ 50 km s−1 (NGC 3593); and others where σg increases to > 100 km s−1 either at the very center (as in NGC 2179, NGC 2775) or over an extended radial range around the center (as in NGC 3281, IC 724). 4. Mass models Previous authors (Fillmore, Boroson & Dressler 1986; Kent 1988; Kormendy & Westpfahl 1989) noticed that in the bulge of early-type spirals Vg falls below the predicted circular velocity. Such ‘slowly rising’ gas RCs are explained by Bertola et al. (1995) with the argument that random (non-circular) motions are crucial for the dynamical support of the ionized gas: in some galaxies of their S0 sample they measured σg ∼ σ? > ∼ 150 km s−1 over an extended range of radii. We do observe the same phenomenon in some of our early-type spirals (see Fig. 5): this fact prevents us to adopt, for early-type disk galaxies, the inner portion of Vg (r) as the circular velocity on which to perform the mass decomposition. When the high values for the velocity dispersion of the gas are measured only in the very central parts (as in NGC 2179) we can not exclude that this is an effect of rotational broadening due to the seeing smearing of the steep velocity gradient. −1 At larger radii where σg < ∼ 50 km s , the ionized gas can be considered a tracer of the actual circular velocity. But the limited extension, (0.5–1) R25 (see Table 1), of our Vg (r) makes the derivation of the halo parameters of early-type spirals more uncertain than for later types. In fact, on one hand we lack data at very large radii where only disk and halo affect the circular velocity, on the other hand at small radii (where we can not consider the gas in circular motion) not two (like for

Sc-Sd galaxies), but three mass components will have locally similar behaviors (solid-body like). So, in absence of extended and complete RCs, an Sa mass solution would be degenerate. We therefore have to model the stellar kinematics to determine the galaxy’s total gravitational potential. Then we need to check the derived mass decomposition by comparing the circular velocity, inferred from the model, with Vg at large galactocentric radii. This is necessary to minimize uncertainties on the mass structure obtained from the stellar kinematics. In fact, the uncertain orbital structure of the spheroidal component, consistent with the observed kinematics leads to a degeneracy between velocity anisotropy and mass distribution, which can be solved only through the knowledge of the line-of-sight velocity distribution profiles (Gerhard 1993). Two galaxies of the observed sample, namely NGC 2179 and NGC 2775, are particularly suited to be studied with the three-component mass models, based on stellar photometry and kinematics, at our disposal. They were chosen for their nearly axisymmetric stellar pattern and to not contain kinematically decoupled (as found NGC 3593 and NGC 4698) or triaxial (as found in NGC 4845) stellar components. 4.1. The modeling technique We apply the Jeans modeling technique introduced by Binney, Davies & Illingworth (1990), developed by van der Marel, Binney & Davies (1990) and van der Marel (1991), and extended to two-component galaxies by Cinzano & van der Marel (1994) and to galaxies with a DM halo by Cinzano (1995). (For a detailed description of the model and its assumptions, see the above references.) The galaxy is assumed to be axisymmetric. Its mass structure results from the contributions of: (i) a spheroidal component; (ii) an infinitesimally thin exponential disk; and (iii) a spherical pseudo-isothermal dark halo with density distribution ρ(r) = ρ0 / 1 + (r/rh )2 . The mass contribution of the ionized gas is assumed to be negligible at all radii. The spheroidal and disk components are supposed to have constant M/L ratios. The total potential is the sum of the (numerically derived) potential of the spheroid plus the (analytical) potentials of the disk and the halo. The stellar distribution function f is assumed to depend only on two integral of motion [i.e., f = f (E, Lz )]. In these hypotheses the Jeans equations for hydrostatic equilibrium form a closed set that, once solved in the total potential, yields the dynamical quantities to be compared with the observed kinematics, once projected onto the sky plane. To obtain the potentials of the bulge and the disk, we proceed through several steps. (a) First, the bulge surface brightness is derived from the total one by subtracting the disk. Then, it is deprojected by means of Lucy’s algorithm to yield the 3-D luminosity density which, via the M/L ratio, gives the 3-D mass density of the bulge. Finally, solving Poisson’s equation through multipole expansion, we derive the bulge potential (Binney et al. 1990). (b) The exponential disk parameters (scale length rd , central surface brightness µ0 , and inclination i) are chosen ac-


cording to the best-fit photometric decomposition. If rd , µ0 and i are the disk parameters resulting from the photometric decomposition, the best-fit model to the observed stellar kinematics was obtained considering exponential disks with |rd −200 | ≤ rd , |µ0 − 0.3| mag arcsec−2 ≤ µ0 , and |i − 5◦ | ≤ i. These parameters determine the surface brightness of the disk. Through the disk M/L ratio we obtain the surface mass density of the disk, and then its potential (Binney & Tremaine 1987). We first solved the Jeans equations only for both the bulge and disk components in their total potential, to give in every point of the galaxy the velocity dispersions onto the meridional 2 = σz2 and the mean azimuthal squared velocities vφ2 . plane σR To disentangle the respective contributions of the azimuthal velocity dispersion σφ2 and the mean stellar motion v 2φ to vφ2 , for the bulge we made the same hypotheses of Binney et al. (1990) while for the disk we followed Cinzano & van der Marel (1994) respectively. Part of the second azimuthal velocity moment vφ2 in the bulge is assigned to the streaming velocity vφ as in Satoh (1980). The azimuthal velocity dispersion σφ2 in the disk is as2 sumed to be related to σR (which is assumed in turn to have 2 and scale-length an exponential fall-off with central value σR,0 rσ ) according to the epicyclic theory (cfr. Binney & Tremaine 1987). In the framework of Cinzano & van der Marel (1994), we have to take into account the effects of seeing, of finite slitwidth and pixel-size in data acquisition, and of Fourier filtering in data reduction (notably the wavenumber range, as discussed in Sect. 2.1.), in order to compare the sky-projected model predictions with the observed stellar kinematics. We interpret the discrepancy between the model’s circular velocity and the observed gas rotation in the outer regions as due to the presence of a DM halo. In this case, the Jeans equations have to be solved again, taking the halo into account, too. By introducing the DM halo, the number of free parameters of the model increases to ten. They are: k, the local rotation anisotropy parameter of the bulge; the M/L ratios of the bulge and the disk; the disk central surface brightness, scale length and inclination; the central value and scale length of the disk’s second radial velocity moment; and the halo’s central mass density and core radius. To reduce the number of free parameters, in the following we consider only three-component models having same best-fit parameters as no-halo models except for the bulge and disk M/L ratios. We choose the fit parameters in order to simultaneously reproduce the stellar kinematics at all radii as well as Vg at large radii. The modeling technique described above derives the 3-D distribution of the luminous mass from the 3-D luminosity distribution inferred from the observed surface photometry. For this reason, in the central regions we take into account the seeing effects on the measured photometrical quantities (surface brightness, ellipticity and cos 4θ deviation profiles). We derive for NGC 2179 and NGC 2775 the seeing cutoffs rµ and r , defined by Peletier et al. (1990) as the radii beyond which the seeing-induced error on the profile is lower than, respectively, 0.05 mag arcsec−2 in surface brightness and 0.02

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in ellipticity. They have expressed rµ and r for a de Vaucouleurs profile as a function of the seeing FWHM, the effective radius re and the ellipticity . For the bulge, we obtained re and , and the corresponding seeing cutoffs rµ and r , following an iterative procedure. We started by performing a standard bulgedisk decomposition with a parametric fit (e.g. Kent 1985): we decomposed the observed surface-brightness profile on both the major and the minor axis as the sum of a de Vaucouleurs bulge of surface-brightness profile " # 1/4 r −1 , (2) µb = µe + 8.3268 re plus an exponential disk of surface-brightness profile r . µd = µ0 + 1.0857 rd

(3)

We assumed the minor-axis profiles of each component to be the same as the major-axis profiles, with values scaled by a factor 1 − = b/a. A least-squares fit of the model to the photometric data provided re , µe and of the bulge, µ0 , rd of the disk, and the galaxy inclination i. The values of re and were used as a starting input to derive rµ and r . Following van der Marel (1991), the ellipticity and the cos 4θ Fourier coefficients were kept constant within r to their value at r , and the surface-brightness profile was truncated at its value at rµ . A new parametric bulge-disk decomposition was then performed on the truncated photometric data. The resulting new values of the effective radius and ellipticity of the bulge were in turn used to obtain a further estimate of rµ and r . The surface photometry was again modified according to these new values, and then another parametric fitting was done. The process was repeated up to convergence. A least-squares fit to µ(r) in the bulge-dominated region beyond rµ was performed using the 2-D brightness distribution resulting from the 3-D luminosity density given for a spherical body by: (i) a modified Hubble law (Rood et al. 1972): " 2 #− 32 r (4) jhu (r) = j0 1 + ahu where j0 and ahu are respectively the central luminosity density and the core radius; (ii) a Jaffe law (Jaffe 1983): 1 Ltot aja 2 (5) jja (r) = 3 4πaja r (1 + r/aja )2 where Ltot and aja are the total luminosity and the half-light radius; (iii) a Hernquist law (Hernquist 1990): jhe (r) =

1 Ltot ahe 2π r (r + ahe )3

(6)

where Ltot and ahe are the total luminosity and a scale radius.

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Fig. 7. The deprojection of the surface brightness of the spheroidal component of NGC 2179. The right panel shows the difference µmodel − µobs after each Lucy iteration (dashed lines) starting from an initial Hernquist fit to the actual NGC 2179 bulge brightness. The residuals are shown for four axes (major through minor axis: top through bottom). For each set of curves: the solid line corresponds to the projected adopted model for 3-D luminosity density; and the dotted line corresponds to a perfect deprojection. At each iteration if the model is brighter than the galaxy, the corresponding dashed or continuous curve is below the dotted line. In the left panel the final 3-D luminosity density profile of the spheroidal components of NGC 2179 is given in units of 1010 L kpc−3 for the same four axes (minor through major axis: innermost through outermost curve)

Fig. 6. The NGC 2179 R−band surface brightness, ellipticity and cos 4θ coefficient profiles as a function of radius along the major axis. The arrows in the surface brightness and in the ellipticity panels indicate the position of the seeing cutoff radii rµ and r . The dashed curve in the upper panel is the surface brightness exponential profile of the disk component of the best fit model to the stellar kinematics

The best fit was achieved for NGC 2179 with a Hernquist profile and for NGC 2775 with a modified Hubble profile. We used them to extrapolate the µ(r) profiles of the two galaxies to r < rµ . After subtracting the disk contribution from the total surface brightness, the 3-D luminosity density of the bulge was obtained starting Lucy’s iterations from a flattened Hernquist model for NGC 2179 and from a flattened modified Hubble model for NGC 2775. The radial profiles of these flattened models are derived respectively from Eqs. 6 and 4 by replacing r with (q 2 R2 + z 2 )1/2 where q is the flattening and R, z cylindrical coordinates. 4.2. The modeling results In this section we present the mass models of NGC 2179 and NGC 2775. 4.2.1. NGC 2179 In Fig. 6 we show the R-band surface brightness (µR ), ellipticity () and cos 4θ Fourier coefficient of the isophote deviations from elliptical, as a function of radius along the major axis.

The seeing cutoffs are rµ = 3.00 0 and r = 5.00 2. The corresponding best-fit parameters obtained from the photometric decomposition are: µe = 21.0 R−mag arcsec−2 , re = 12.00 4, b = 0.58 for the de Vaucouleurs bulge; µ0 = 21.8 R−mag arcsec−2 , rd = 23.00 5, d = 0.29 for the exponential disk. (Taking into account the photometric bulge-disk decomposition, the exponential disk yielding the best-fit model to the observed stellar kinematics has µ0 = 21.7 R−mag arcsec−2 , rd = 23.00 7 = 4.1 kpc, and i = 45◦ ; see dashed curve in Fig. 6). We then subtract the disk contribution from the total surface brightness. The residual surface brightness is the contribution of the spheroidal component. The difference between the surface brightness of the spheroid and that obtained projecting the 3-D luminosity distribution of each of the four Lucy iterations (including the initial flatted Hernquist model) is shown in Fig. 7 (right panel) along NGC 2179’s major, minor and two intermediate axes. (The r.m.s. residual of the last Lucy iteration corresponds to 0.06509 mag arcsec−2 ). The 3-D luminosity density of the final bulge model along the same four axes is also presented in Fig. 7 (left panel). We fold vg and v? around their respective centers of symmetry. In order to determine the latter, we fit a suitable odd function to both RCs independently: this yields the position of the kinematical center of the curve, r0 , and the heliocentric velocity of the galaxy, V . We find V = 2885 ± 10 km s−1 for both gas and stars, and r0,g = +0.00 5 ± 0.00 3 and r0,? = +0.00 6 ± 0.00 3. We then fold σg and σ? around the kinematical center of the respective component.


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Fig. 8. Predicted and observed stellar kinematics of NGC 2179. The filled triangles and the open squares represent data derived for the approaching SE side and for the receding NW side respectively. The continuous and the dashed lines are the model stellar velocities (upper panel) and velocity dispersions (lower panel) obtained with and without the dark halo component respectively Fig. 10. The NGC 2775 r−band surface brightness and the ellipticity profiles as a function of radius along the major axis (Kent 1988). The dashed curve in the top panel is the surface brightness exponential profile of the disk component of the best fit model to the stellar kinematics

Fig. 9. In the upper panel the predicted circular velocity and the observed gas rotation velocity of NGC 2179 are shown. The filled triangles and the open squares represent data derived for the approaching side and for the receding side respectively. The continuous and the dashed lines are the total circular velocities derived from the stellar kinematics with and without the dark halo component respectively. In the lower panel the maximum contribution of the luminous matter (dashed line) to the total circular velocity (continuous line) is plotted if a dark matter halo (dotted line) is considered

The best-fit model to the observed major-axis stellar kinematics is shown in Fig. 8. Its parameters are as follows. The bulge is an oblate isotropic rotator (k = 1) with (M/LR )b = 6.1 (M/LR ) . The exponential disk has σ? (r) = 168 e−r/rσ km s−1 with scale-length rσ = 23.00 2 = 4.0 kpc), and (M/LR )d = 6.1 (M/LR ) . The derived bulge and disk masses are Mb = 7.0 · 1010 M and Md = 2.5 · 1010 M , adding up to a total (bulge + disk) luminous mass of MLM = 9.5 · 1010 M . The DM halo has ρ0 = 6.9 · 10−2 M pc−3 and rh = 2400 = 4.2 kpc, which correspond to an asymptotic

rotation velocity V∞ = 257 km s−1 ; its mass at the outermost observed radius is MDM = 6.5 · 1010 M . The ratio between the mass-to-light ratios of the stellar components in the models with and without the DM halo is 0.9. The comparison between the observed rotation of the ionized gas and the true circular velocity, inferred from stellar kinematics, is given in the upper panel Fig. 9. It shows that a DM halo is unambiguously required to explain the rotation at large radii (r ≥ 2500 ). This result hinges on accuracy of the gas kinematics data beyond 4000 mostly derived from Hα line measurements. In NGC 2179, the gas rotation does provide the circular velocity at all radii. The contribution of the DM halo to NGC 2179 circular velocity as function of radius is plotted in lower panel of Fig. 9. 4.2.2. NGC 2775 In Fig. 10 we show µr (r) and (r) along the major axis (Kent 1988). The seeing FWHM for the Kent (1988) data is 2.00 3. We derive the seeing cutoffs rµ = 4.00 0 and r = 5.00 2. As no cos 4θ profile is available, we assume it is zero throughout. The photometric model is improved by taking into account an outer dust lane surrounding the spiral pattern of the galaxy. (This appears as a thin dust ring at about 8000 from the center, and is visible on panels 78 and 87 of the CAG, see Sandage & Bedke 1994). As a fitting function for the disk component, we use an exponential profile weighted by an absorption ring. We assume the section of the dust ring to have a Gaussian radial profile,

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Fig. 11. Same as Fig. 7, but for NGC 2775 and starting from a flattened modified Hubble model for the spheroidal component

defined by central intensity maximum absorption Ar , a center rr and a scale-length σr . This leads to a disk light contribution r−rr 2 (7) Id,ring (r) = Id (r) 1 − Ar e−( σr ) The best-fit parameters resulting from the improved photometric decomposition are: µe = 22.0 r-mag arcsec−2 , re = 53.00 0, b = 0.10 for the de Vaucouleurs bulge; µ0 = 20.7 r-mag arcsec−2 , rd = 40.00 5, d = 0.28 for the exponential disk; and Ar = 0.25, rr = 8500 and σr = 2000 for the dust ring. The exponential disk yielding to the best-fit model to the observed stellar kinematics has µ0 = 20.7 r-mag arcsec−2 , rd = 40.00 0 = 3.0 kpc, and i = 44◦ (see Fig. 10). The surface brightness of the exponential disk in Fig. 10 is subtracted from the total surface brightness. The fit to the spheroidal component’s deprojected surface brightness is obtained after four Lucy iterations from an initial flatted modified Hubble model (The r.m.s. residual is 0.03209 mag arcsec−2 , see Fig. 11). The 3-D luminosity density of the final bulge model along the major, minor and two intermediate axes is also shown in Fig. 11. We find vg and v? to have same center of symmetry at r0,g = r0,? = +4.00 0 ± 0.00 3 and V = 1350 ± 10 km s−1 . The velocity dispersion profiles are folded around the kinematical center. The best-fit model to the observed major-axis stellar kinematics is shown in Fig. 12. Its parameters are as follows. The bulge is an oblate isotropic rotator (k = 1) with (M/Lr )b = 5.2 (M/Lr ) . The exponential disk has σ? (r) = 130 e−r/rσ km s−1 with scale-length rσ = 17.00 5 = 1.3 kpc), and (M/Lr )d = 7.0 (M/Lr ) . The derived bulge and disk masses are Mb = 8.5 · 1010 M and Md = 6.1 · 1010 M , so the total (bulge + disk) luminous mass is MLM = 14.6 · 1010 M . We kept the ratio between the bulge and disk M/L fixed at the value 1.36 (see Kent 1988). The DM halo has central density ρ0 = 5.8 · 10−2 M pc−3 and core radius rh = 6000 = 4.6 kpc, which correspond to an asymptotic rotation velocity V∞ = 258 km s−1 ; its mass at the outermost observed radius is MDM = 3.1 · 1010 M . (The latter should be considered an upper limit because the inner kinematics can be explained with no DM halo). Contrary to NGC 2179 in this case we kept the same

Fig. 12. Same as Fig. 8, but for NGC 2775. The filled triangles and the open squares represent data derived for the receding SE side and for the approaching NW side respectively. The dotted line is the model kinematics for the spheroidal component

mass-to-light ratios of the stellar components in the models with and without the DM halo. For |r| > 6500 the presence on the equatorial plane of the dust ring, which reduces the light contribution of the (fasterrotating) disk stars of a further ∼ 25%, causes the observed stellar kinematics to be more affected by the (slower-rotating) bulge stars. In this picture as shown in Fig. 12, our bulge model agrees with the observed drop in velocity and the rise in velocity dispersion. NGC 2775 is a dust-rich system, as can be inferred from its dust-to-HI mass ratio (Roberts et al. 1991), which is ∼ 12 times larger than the mean S0/Sa values (Bregman, Hogg & Roberts 1992). Although the total luminous mass found by Kent (1988) MLM = 14.3 · 1010 M (with H0 = 75 km s−1 Mpc−1 ) is in good agreement with ours, his mass decomposition differs from ours. He assumed only the bulge to have an analytical µ(r) (a de Vaucouleurs law with µe = 21.0 mag arcsec−2 , re = 22.00 9, b = 0.12), while the disk µ(r) was taken to be the bulge-subtracted major-axis profile. Kent’s approach is opposite to ours. We assume the disk to have an analytical µ(r), and the bulge µ(r) to be the residual surface brightness after subtracting the disk (assuming no a priori analytical expression or fixed axis ratio). Scaled to our assumed distance, the luminosity of Kent’s bulge is ∼ 31% of ours, while our disk luminosity is ∼ 43% of Kent’s. Van der Marel et al. (1991) studied the effects of a cos 4θ deviation on the kinematics of NGC 4261. They found that changing the cos 4θ Fourier component from zero to ±0.02 produces variations of ∼ 2% in velocity dispersion and ≤ 10% in rotation velocity. Fig. 13 shows the stellar kinematics of NGC 2775 in the case of slightly disky (cos 4θ = +0.02) and slightly boxy (cos 4θ = −0.02) isophotes (solid and dotted line, respectively). The disky model rotates faster and has a lower σ? than the boxy model in the inner 2500 (1.9 kpc). The differences in V? and in σ? between the two models are < 10 km s−1 : this means that, in the observed range of values, a difference of 0.04 in cos 4θ


Fig. 13. Predicted stellar kinematics for NGC 2775 with fixed cos 4θ = +0.02 (solid line) and fixed cos 4θ = −0.02 (dotted line) at all radii

coefficients corresponds to a difference of < 12% in velocities and < 7% in velocity dispersions. However, these uncertainties are immaterial to our results on the mass structure of NGC 2775. The comparison between Vg and the true circular velocity inferred from the stellar kinematics is shown in the upper panel of Fig. 14. It shows that a DM halo is not strictly required to explain the rotation at large radii (r ≥ 3500 ). The contribution of the DM halo to NGC 2775 circular velocity as a function of radius is plotted in the lower panel of Fig. 14. Inside 3000 on the receding arm, V? ' Vg and σ? > σg ' 50 km s−1 . This rules out the case that the gas kinematics is dominated by random motions, and leads us to speculate that we are looking at gas rotating on a non-equatorial plane. We suggest this is the signature of a past external acquisition (possibly from the companion galaxy NGC 2777) of gas still not completely settled onto the disk plane. 5. Discussion and conclusions We have presented the ionized-gas and stellar kinematics, measured along the major axis, for a sample of six early-type spiral galaxies. (Due to the high values of σg in their inner regions, the gas RCs can not be used as circular-velocity curves.) For NGC 2179 and NGC 2775, we have modeled both the stellar and the gaseous kinematics to derive the mass contribution of the luminous and dark matter to the total potential, improving on the efforts by Kent (1988) from gas kinematics alone. We have found that the innermost kinematics (r < 2RD ) is very well and uniquely reproduced by taking into account the two luminous components. In the (very luminous) early-type spirals considered here, there is a large inner region in which (essentially) light traces the mass and the DM is a minor mass component. This is agreement with the ‘weak’ maximum disk paradigm proposed by Persic & Salucci (1990), but in disagreement with the claim by Courteau & Rix (1998) according to which in the most luminous spirals DM is a protagonist at essentially any radii.

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Fig. 14. Same as Fig. 9, but for NGC 2775. The filled triangles and the open squares represent data derived for the receding SE side and for the approaching NW side respectively

More in detail we have found that in NGC 2179 the combined stellar and gaseous rotation data (measured out to about Ropt ) require the presence of a massive dark halo. In NGC 2775, more luminous and massive than NGC 2179, we can rule out a significant halo contribution out to 0.6 Ropt . This result complies with the general trend of mass distribution known for later spirals (Persic et al. 1996). Salucci & Persic (1997), considering a large number of galaxies of mixed morphologies (ellipticals, late spirals, dwarfs, and LSBs), have suggested that the halo structural parameters and the connection between the dark and the luminous matter show a strong continuity when passing from one Hubble Type to another. Ellipticals, considered as luminous spheroids, and spirals, considered as luminous disks, are evidently very different systems, markedly discontinuous in terms of the distribution and global properties of the luminous matter. However, in the structural parameter space, ellipticals and spirals are contiguous, the main difference being that the former are more concentrated in both the dark and luminous components, probably due to the baryons’ dissipational infall being deeper in ellipticals than in spirals (e.g., Bertola et al. 1993). If so, it is hardly surprising that Sa galaxies, being in some sense intermediate systems consisting of a luminous spheroid embedded in a luminous disk, fit in the regularity pattern of the dark-to-visible mass connection shared by ellipticals and spirals. In Fig. 15 we plot our derived dark-to-visible mass ratios at the farthest measured radii for NGC 2179 and NGC 2775 (filled circles) onto the distribution, derived by Salucci & Persic (1997) for galaxies with the same visible mass. The agreement is good. Even if the present result on early-type spirals is preliminary and without pretending to draw general conclusions from one particular case, it nevertheless seems to agree with the idea that, for galaxies of all morphological types, the dark-to-luminous mass ratio at any given radius depends only on the (luminous) mass of the galaxy.

686


Fig. 15. The dark-to-luminous mass ratio as a function of radius (normalized to Ropt ) for late spirals of same stellar mass as NGC 2179 and NGC 2775 (solid lines), compared with our derived values for NGC 2179 and NGC 2775 (filled circles) Acknowledgements. We are indebted to R.P. van der Marel for providing his f (E, Lz ) modeling software which became the basis of our modeling package. We also thank R. Falomo for providing some photometric data reduction tools. We are most grateful to the Vatican Observatory Research Group for allocating the observing time. Particular thanks go to R. Boyle, S.J. for his help during the observing run at the VATT. The research of AP was partially supported by an Acciaierie Beltrame grant. JCVB acknowledges a grant from Telescopio Nazionale Galileo and Osservatorio Astronomico di Padova. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.

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